The oscillation of higher-order differential equations with deviating arguments

In this paper, some new criteria for the oscillation of higher-order functional differential equations of the form Lnx(t)+F(t,x(g(t)))=0 , n is even are established. Some of our results are obtained via comparing it with second-order ordinary linear and first-order delay differential equations. The oscillation of this equation when n is odd is also considered. Then, we shall use the obtained results to study the oscillatory behavior of the neutral functional differential equations of the form Ln(x(t)+c(t)x(τ(t)))+F(t,x(g(t)))=0 , n is even and the damped functional differential equations of the type Lnx(t)+H(t,x(g(t)), ddtx(h(t)))=0 n is even The obtained results extend, improve, and correlate a number of existing criteria.

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